1.7 Exponents and Order of OperationsExponential Notation:Shorthand for writing repeated multiplication of the same number.

8888 48 333 33

1010101010 510

44444455 62 45

24 44 57 77777 523 6102 666661010222

Order of Operations:The order in which mathematical operations must be performed.

PEMDASP → ParenthesisE → ExponentsM → MultiplicationD → DivisionA → AdditionS → Subtraction

1.7 Exponents and Order of Operations

Order of Operations:4839 22348 24 32710

PEMDAS

25

4827 227

4348 416

64

24 323 9281

188199

1.7 Exponents and Order of Operations

Order of Operations: 64242036 2 53636

PEMDAS

536 518

23

6482036 2 641236 2

6161236 6163

619 13

1.7 Exponents and Order of Operations

Order of Operations:

232

32825 2

PEMDAS

23232825 2

1232825 2

292825 291625 2941

23216

1.7 Exponents and Order of Operations

1.8 Variables, Algebraic Expressions and Equations

Definitions:Variable - A letter that represents a number or a set of numbers.Algebraic Expression - A combination of operations on variables and numbers.

Equation- Two algebraic expressions that are equal.

Solution- The value or values for the variable that make an equation true.

Evaluate- Substituting a value for the variable of an expression or equation and calculating the result.

72 isxifx

Evaluate the following:

27 5

483 yandxifxy

384 5420

1866

yandxifx

y

6

618 6

24 4

1.8 Variables, Algebraic Expressions and Equations

1225 3 xandzifxz

Evaluate the following:

121225 3 xandzif

121225 3 xandzif

OR

1825

11718

1.8 Variables, Algebraic Expressions and Equations

41

9

325

Fif

F

Evaluate the following:

9

32415

9

95

9

45 5

1.8 Variables, Algebraic Expressions and Equations

663 y

Determine whether 8 is a solution of the equation

6683

623

66True statement,

8 is a solution.

1.8 Variables, Algebraic Expressions and Equations

3445 n

Determine which numbers in the set { 10, 6, 8} are solutions of the equation

344105

True statement,

6 is a solution.

34450

3454False statement,

10 is not a solution.

34465

34430

3434

34485

34440

3444False statement,

8 is not a solution.

1.8 Variables, Algebraic Expressions and Equations

Write an Algebraic Expression. Use x to represent “a number.”

Twice a number x2

6

x

x8

x10

8 increased by a number

10 minus a number

10 subtracted from a number 10x

The quotient of a number and 6 or 6x

1.8 Variables, Algebraic Expressions and Equations

2.1 Introduction to Integers

Definitions:Positive numbers – All numbers greater than zero. The positive sign states that the number is to the right of zero on a number line.

Negative numbers – All numbers less than zero. The negative sign states that the number is to the left of zero on a number line.

Signed numbers – Positive numbers, negative numbers and zero.

2.1 Introduction to Integers

Definitions:Integers – All positive numbers, negative numbers and zero, but no fractions or decimals.

Negative integers Positive integersZero

NOTE: Zero is neither positive or negative!

2.1 Introduction to Integers

Graphing Integers

Graph -4, -1, 2, and -2 on the number line.

Negative integers Positive integersZero

2.1 Introduction to IntegersRepresenting Position with Integers

Use an integer to represent each of the following positions.

4. The world’s deepest colony of bats is located in a New York zinc mine at a depth of 3805 feet.

feet460,12

2. The tamarack tree survives at the edge of the arctic tundra at 85 degrees below zero.

1. The wreck of the Titanic was located at 12,460 feet below sea level.

85

feet4229

feet3805

3. The bottom of Crater Lake is located at 4,229 feet above sea level.

2.1 Introduction to Integers

Comparing IntegersFor any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number.

Inequality Symbols

“is greater than”

“is less than”

“is greater than or equal to”

“is less than or equal to”

2.1 Introduction to Integers

Comparing IntegersInsert or between each pair of numbers to

make a true statement.

50 33 127

784521 79126

2.1 Introduction to Integers

Absolute Value of a NumberThe distance a number is from 0 on the number line.

22 1522 15

The distance a number is from 0 is always 0 or a positive distance – NEVER a negative value.

The symbol or operator for the Absolute Value is: | |

586 586

0 0 37 37

2.1 Introduction to Integers

Opposite NumbersTwo numbers that are the same distance from zero but are on opposite sides of zero.

Which of the following represent opposites?YES

YES

NO

2.1 Introduction to Integers

Opposite Numbers

14 14

Find the opposite values of the following numbers:

9 9 58 58

2.1 Introduction to Integers

Mixed Practice

62 62

7 7

4 4 43 43

8 8

10: xifxEvaluate 10 10